Convergence of the Nelder-Mead simplex method to a nonstationary point
Convergence of the Nelder-Mead simplex method to a nonstationary point
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DOI：
10.1137/s1052623496303482
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发表时间：
1998-12-21
影响因子：
3.1
通讯作者：
Mckinnon, KIM
中科院分区：
文献类型：
--
作者：
Mckinnon, KIM
本文通过一系列示例分析了 Nelder-Mead 单纯形法的行为，这些示例导致该方法收敛到非平稳点。所有示例都使用两个变量的连续函数。该函数族包含最多具有三个连续导数的严格凸函数。在所有示例中，该方法重复应用内部收缩步骤，同时最佳顶点保持固定。单纯形趋向于与最陡下降方向正交的直线。结果表明，对于具有超过三个连续导数的函数，这种行为不会发生。分析了算例的稳定性。
This paper analyzes the behavior of the Nelder-Mead simplex method for a family of examples which cause the method to converge to a nonstationary point. All the examples use continuous functions of two variables. The family of functions contains strictly convex functions with up to three continuous derivatives. In all the examples the method repeatedly applies the inside contraction step with the best vertex remaining fixed. The simplices tend to a straight line which is orthogonal to the steepest descent direction. It is shown that this behavior cannot occur for functions with more than three continuous derivatives. The stability of the examples is analyzed.